Prof. Roy Welsch (MIT)

In multivariate analysis, estimating the location vector and dispersion matrix is a fundamental step
for many applications. Classical sample mean and covariance estimates are very sensitive to outliers,
and therefore their robust counterparts are considered to overcome the problem. For p-dimensional
data, the robust mean vector requires estimating p parameters, while the robust covariance matrix
requires estimating p(p-1)/2 parameters, and the resulting matrix needs to be positive definite.
Therefore, covariance estimation is more challenging than mean estimation. We propose a new
robust covariance estimator using the regular vine dependence structure and pairwise robust partial
correlation estimators. The resulting positive definite robust covariance estimator delivers high
performance for identifying outliers under the Barrow Wheel Benchmark for large high dimensional
datasets. Finally, we demonstrate a financial application of active asset allocation using the proposed
robust covariance estimator, and the proposed estimator delivers better results compared to many
existing asset allocation methods. (Joint work with Zhe Zhu)